I used to visit that part of the country frequently on business. The Smithsonian and the usual government sights are all well worth doing but boy they can get crowded in regular daytime hours. My favorite sites in the Washington area were a bit outside the city, like in Alexandria and south to Mt. Vernon. If you take 66 on the west side to go visit the Manassas (Bull Run) Civil War battlefield site, you will pass by the NRA museum, both are great sights to see. Another must-see is George Washington's Mount Vernon.
I really enjoyed visiting George Washington's grist mill and distillery, the mill is reconstructed and when I was there it was functional and they ground corn for us. It is impressively automated for a 1780's vintage mill, only a few people were needed to run it. It has some pretty good sized millstones, and it was impressive to see the power of that big waterwheel when it was engaged - torque a-plenty, the stones accelerated from rest so fast they just boomed to life and emitted a big puff of dust. Another great sight is the George Washington National Masonic memorial and museum.
For me the most impressive sights in DC were on the mall. I tried not to get too close to the Capitol because the urge to horsewhip politicians is just overpowering, they ought to hand whips out to the visitors like brochures. But I digress.... the Washington monument is just awesome, so much bigger in person than one might expect. The Lincoln memorial is overwhelming, the statue of him sitting has such a powerful presence it is hard to describe.
For me the very early morning hours were always my favorite times to visit the memorials, they are usually deserted at sunrise and you have time for reflection. Seeing the sunrise there can be a near religious experience. The war memorials are also phenomenal. The Marine Corps memorial of the flag-raising is huge, pictures simply cannot do it justice. The Vietnam Wall will leave those of a certain age very powerfully affected -- looking up names on the wall of people that you knew, and then stepping back to look at the stark reality of more than 58,000 listed. It puts it in a whole different perspective.
One morning I was walking in the midst of a very dense fog, it was dark and quiet and I could not see more than a few yards. As dawn was breaking and light began to filter through the fog, right beside me I could see ghostly figures of soldiers looming out of the dark, larger than life and so realistic it made me stop for a few seconds wondering if there was some operation underway, then I realized it was the Korean War memorial. It has statues of soldiers on patrol, being there alone in the brightening dawn with them was very powerful. I stood there staring at them for a long time thinking about my relatives who fought in that war.
Sorry for the long screed, those are just a few of the things I found most memorable on my trips up there. You will have a blast, so much to see and do!
PS - lots of bums and nuts wander around the mall area, if you are on foot exploring at night you should be careful and keep an eye open.